Polarization element and optical device using polarization element

ABSTRACT

A high performance polarization splitting element and an optical device using the polarization splitting element are provided. According to an embodiment of the present invention, the optical device includes a first periodic structure having a period shorter than a wavelength of used light, a second periodic structure which has a period shorter than the wavelength of the used light and in which a direction of the period is orthogonal to or substantially orthogonal to that of the first periodic structure, and a pair of optical elements disposed so as to sandwich the first periodic structure and the second periodic structure. The second periodic structure is adjacent to the first periodic structure. The first periodic structure and the second periodic structure transmit light having first polarization direction and reflect light having second polarization direction orthogonal to the first direction, and the second polarization direction is substantially parallel to one of the periodic direction of the first periodic structure and the periodic direction of the second periodic structure.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a polarization element, and moreparticularly to an optical device including the polarization elementsuch as an image pickup optical system, a projection display device(projector), an image processing apparatus, or a semiconductormanufacturing apparatus.

2. Related Background Art

Up to now, a polarization splitting element using, for example, adielectric multi-layer film has been known. As shown in FIG. 37, thepolarization splitting element allows P-polarized light 18 incident onmulti-layer film 17 to transmit through the film at a Brewster's angleas light 19 shown in FIG. 37, and reflects S-polarized light 20 byinterference of the multi-layer film as light 21.

The multi-layer film is constructed by stacking dielectric layers havingdifferent refractive indices. Assume that a layer having a highrefractive index nH is referred to as a layer H and a layer having arefractive index nL lower than the refractive index nH is referred to asa layer L. In general, a Brewster's angle θ_(B) between two media havingrefractive indices n₁ and n₂ is expressed by the expression (1). Ofincident light beams at this angle, a P-polarized light component passesthrough all the dielectric layers.tan θ_(B) =n ₂ /n ₁  (1)

In order to realize the polarization splitting element, it is necessaryto establish a relationship between the refractive indices and theangle, in both a prism medium and an interface between the layer H andthe layer L. Therefore, it is necessary to satisfy the followingrelational expression (2) between a refractive index n_(p) of the prismmedium and refractive indices n_(H) and n_(L) of two dielectric mediacomposing a thin film. $\begin{matrix}{n_{p} = \sqrt{\frac{n_{H}^{2}n_{L}^{2}}{\sin^{2}{\theta_{B}\left( {n_{H}^{2}n_{L}^{2}} \right)}}}} & (2)\end{matrix}$

With respect to the S-polarized light, a reflective film by virtue ofmulti-layer film interference is realized using reflection on theinterface due to the refractive index difference between the refractiveindices n_(H) and n_(L) of a high refractive index medium and a lowrefractive index medium, respectively. A film thickness of each of thelayers is optimized and 20 to 40 layers are stacked. Therefore, it ispossible to realize a reflective film that causes reflection over theentire visible light region. With respect to the S-polarized light, awide-angle characteristic and a wide-wavelength characteristic can bedesigned by increasing the number of layers of the film. On the otherhand, transmittance with respect to the P-polarized light depends on therefractive indices between the media and the incident angle, so that thetransmittance does not depend on a change in film thickness. The morethe number of layers increases, the more reflectance with respect to theP-polarized light due to a deviation from the Brewster's angleincreases. Therefore, wavelength and angle characteristics of thetransmittance deteriorate.

A polarization splitting element in which a birefringent adhesive issandwiched between prisms as described in U.S. Pat. No. 5,042,925 hasbeen known as a polarization splitting element that does not use themulti-layer film. This uses a difference between refractive indices foran ordinary ray and an extraordinary ray of the birefringent material.Although the difference of refractive indices therebetween is small, alarge incident angle of about 60° is set to totally reflect one of thepolarized light beams in a selective manner, thereby realizingpolarization splitting.

When the total reflection is to be caused, it is necessary that theincident angle be equal to or larger than a critical angle θ_(c). Thecritical angle θc is expressed by the following expression (3).sin θ_(C) =n ₂ /n ₁  (3)

There has been known a polarization splitting element usingbirefringence in which a multi-layer film is etched to obtain aone-dimensional grating as shown in FIG. 36. The multi-layer film inwhich layers H 15 such as TiO₂ layers and layers L 16 such as SiO₂layers are alternately stacked is etched to obtain the one-dimensionalgrating. When a period of the grating is made equal to or shorter than awavelength of used light, the grating exhibits a birefringentcharacteristic with respect to incident light.

Such a birefringent characteristic caused depending on the structure ofmatter is called structural birefringence. The polarization splittingelement can be realized by combining materials of the multi-layer film,and suitably setting a grating shape. In this specification, a structurehaving a period shorter than a wavelength λ of the used light, such asthe one-dimensional grating, is referred to as a sub-wavelengthstructure (SWS).

The used light in this specification indicates light having a wavelengthrange corresponding to an optical element to be used. For example,assume that light beam from a light source which is made incident on anoptical element to be used for visible light has a wide wavelength band,more specifically, includes light other than the visible light, such asultraviolet light or infrared light in addition to the visible light. Inthis case, the light other than the visible light is also made incidenton the optical element. Even in such a state, assume that the used lightfor the optical element to be used for visible light is visible light.The visible light is light having a wavelength of within a range ofabout 400 nm to 700 nm.

A refractive index of the SWS grating can be treated as an effectiverefractive index. In a grating as shown in FIG. 10A, assume thatpolarized light in a periodic direction of the grating is TM polarizedlight and polarized light in a direction orthogonal to the periodicdirection is TE polarized light. Here, there has been known thateffective refractive indices n_(TE) and n_(TM) with respect to therespective polarized lights in a one-dimensional grating in which mediahaving refractive indices, n₁ and n₂, are repeated at a width ratio ofa:b, are generally expressed by the expressions (4) and (5).$\begin{matrix}{{{TE}\quad n_{TE}} = \sqrt{\frac{{an}_{1}^{2} + {bn}_{2}^{2}}{a + b}}} & (4) \\{{{TM}\quad n_{TM}} = \sqrt{\frac{a + b}{{a/n_{1}^{2}} + {b/n_{2}^{2}}}}} & (5)\end{matrix}$Here, n_(TE)>n_(TM) is satisfied regardless of the ratio of a:b.

In the one-dimensional grating, assume that the medium of n1 is adielectric and the medium of n2 is air. When a ratio of a dielectricwidth to a grating pitch is set as a filling factor f, the fillingfactor f is expressed by the expression (6). In this example, etching isperformed such that the filling factor becomes about 0.5.f=a/(a+b)  (6)

FIG. 10B is a graph showing a change in effective refractive indexrelative to the filling factor f of TiO₂ in a grating in which themedium of n1 is TiO₂ and the medium of n2 is air. Similarly, FIG. 10C isa graph showing a change in effective refractive index in a grating inwhich the medium of n1 is SiO₂. As is apparent from the graphs, adifference between refractive indices of the layer H and the layer L inthe TE direction is larger and a difference between refractive indicesof the layer H and the layer L in the TM direction is smaller. When asuitable prism medium is used, a Brewster's angle condition is satisfiedin the TM direction, with the result that the grating can transmit theP-polarized light. A thickness of each of the layers is independent ofthe Brewster's angle condition. When a film thickness of each of thelayer H and the layer L is optimized, it is possible to form thedielectric multi-layer film. As a result, the dielectric multi-layerfilm is provided with a function for reflecting the S-polarized light,which means that a function of the polarization splitting element isobtained. This improves the degree of freedom of selection of mediasatisfying the Brewster's angle condition with respect to theP-polarized light as compared with the case of the polarizationsplitting element composed of only the dielectric thin film. Therefore,it is possible to simultaneously increase the reflectance for theS-polarized light. Thus, the polarization splitting element covering theentire visible light region can be composed of about 20 layers.

However, in the case of the polarization splitting element using thedielectric multi-layer film, the Brewster's angle condition is used totransmit the P-polarized light. Therefore, the refractive index of aprism glass material and the refractive index of thin film medium arelimited by the expression (1), so it is hard to widen an incident anglecharacteristic. The incident angle characteristic cannot be widened evenif the number of layer is increased.

In the case of the polarization splitting element in which thebirefringent adhesive is sandwiched between the prisms, since thedifference between refractive indices of the ordinary ray and theextraordinary ray of the adhesive is not large, it is necessary to setthe incident angle to about 60° or more for the total reflection.Therefore, applications of usable optical systems are limited. Inaddition, a high polymer material or the like is used for the adhesive,so the polarization splitting element is inferior in terms of heatresistance and light fastness.

The stacked type polarization splitting element having the rectangulargrating using the SWS structure is complex, which increases amanufacturing cost thereof. In addition, the Brewster's angle conditionis used to transmit the P-polarized light, so it is hard to widen theincident angle characteristic as in the case of the dielectricmulti-layer film. In particular, as is apparent from the gratingstructure shown in FIG. 36, the difference between refractive indices ofthe TE direction and the TM direction reduces as the incident angleincreases. Therefore, an increase in reflectance at an incident anglethat exceeds the Brewster's angle is larger than that in the case usingthe dielectric thin film. As a result, there is a limitation on theincident angle characteristic.

In the case of a polarization splitting element used for a liquidcrystal projector or the like, a wide wavelength range which covers theentire visible light region, and a small FNo. for obtaining brightness(that is, a wide angle characteristic) are required.

SUMMARY OF THE INVENTION

The present invention has been made in view of the above-mentionedproblems. An object of the present invention is to obtain a polarizationsplitting element which is suitable for use in a liquid crystalprojector or the like, and has a wide wavelength range that covers isthe entire visible light region and a wide angle characteristic which isusable at a small FNo.

An object of the present invention is to provide a high-performancepolarization splitting element and an optical device using thepolarization splitting element.

According to an aspect of the present invention, there is provided anoptical element, including: a first periodic structure having a periodshorter than a wavelength of used light; and a second periodic structurehaving a period shorter than the wavelength of the used light and inwhich a direction of the period is orthogonal to or substantiallyorthogonal to that of the first periodic structure, the second periodicstructure being adjacent to the first periodic structure, wherein thefirst periodic structure and the second periodic structure transmitlight in a predetermined oscillation direction and reflect light in anoscillation direction orthogonal to the predetermined oscillationdirection.

According to an aspect of the present invention, an optical elementcomprises a first periodic structure having a period shorter than awavelength of used light, a second periodic structure that has a periodshorter than the wavelength of the used light and in which a directionof the period is orthogonal to or substantially orthogonal to that ofthe first periodic structure, the second periodic structure beingadjacent to the first periodic structure, and a pair of optical elementsdisposed so as to sandwich the first periodic structure and the secondperiodic structure, wherein the first periodic structure and the secondperiodic structure transmit light having first polarization directionand reflect light having second polarization direction orthogonal to thefirst direction, and wherein the second polarization direction issubstantially parallel to one of the periodic direction of the firstperiodic structure and the periodic direction of the second periodicstructure.

According to a further aspect of the present invention, in the opticalelement, the used light has a wavelength between 400 nm and 700 nm.

According to a further aspect of the present invention, in the opticalelement, the following conditions are satisfied,n1p<n1s,n2p>n2s,|n1s−n2s|>|n1p−n2p|,where n1p and n1s represent effective refractive indices of the firstperiodic structure with respect to P-polarized light and S-polarizedlight, respectively, and n2p and n2s represent effective refractiveindices of the second periodic structure with respect to the P-polarizedlight and the S-polarized light, respectively.

According to a further aspect of the present invention, in the opticalelement, the following condition is satisfied,0.95<n1p/n2p<1.2,where n1p and n1s represent effective refractive indices of the firstperiodic structure with respect to P-polarized light and S-polarizedlight, respectively.

According to a further aspect of the present invention, in the opticalelement, each of the first periodic structure and the second periodicstructure is made of dielectric.

According to a further aspect of the present invention, in the opticalelement, the dielectric is titanium oxide.

According to a further aspect of the present invention, in the opticalelement, light which is made incident on the first periodic structureincludes a light beam which is made incident on the first periodicstructure at a Brewster's angle determined based on effective refractiveindices of the first periodic structure and the second periodicstructure with respect to P-polarized light.

According to a further aspect of the present invention, in the opticalelement, light which is made incident on the first periodic structureincludes a light beam which is made incident on the first periodicstructure at an angle not smaller than a critical angle determined basedon effective refractive indices of the first periodic structure and thesecond periodic structure with respect to S-polarized light.

According to a further aspect of the present invention, in the opticalelement, the following condition is satisfied,(n1s·d ₁·con θ)/λs<0.5,where n1s represents the effective refractive index of the firstperiodic structure with respect to the S-polarized light, d₁ representsa thickness thereof, λs represents a shortest wavelength of the usedlight which is made incident on the first periodic structure, and θrepresents an incident angle thereof.

According to a further aspect of the present invention, in the opticalelement, the following condition is satisfied,0.2<d ₂ /λs<1.0,where d₂ represents a thickness of the second periodic structure, λsrepresents the shortest wavelength of the used light which is madeincident on the first periodic structure, and θ represents the incidentangle thereof.

According to a further aspect of the present invention, in the opticalelement, each of the first periodic structure and the second periodicstructure is a grating made of dielectric, and the following conditionsare satisfied,0.3<f1<1.0,0.10<f2<0.5,where f1 represents a filling factor which is a ratio between the periodof the first periodic structure and a width of a corresponding gratingand f2 represents a filling factor which is a ratio between the periodof the second periodic structure and a width of a corresponding grating.

According to a further aspect of the present invention, in the opticalelement, the period of the first periodic structure and the period ofthe second periodic structure are different from each other.

According to another aspect of the present invention, an optical devicecomprises an optical element set out in the foregoing, modulation devicefor modulating light emitted from the optical element based on an imagesignal; and a projection optical system for projecting the lightmodulated by the modulation means to a predetermined plane.

According to another aspect of the present invention, an optical elementcomprises a first periodic structure having a period shorter than awavelength of used light, and a second periodic structure that has aperiod shorter than the wavelength of the used light and in which adirection of the period is orthogonal to or substantially orthogonal tothat of the first periodic structure, the second periodic structurebeing adjacent to the first periodic structure,

wherein the period of the first periodic structure and the period of thesecond periodic structure are different from each other.

According to a further aspect of the present invention, in the opticalelement, with respect to a first plane including a periodic direction ofthe first periodic structure and a normal to a plane of the firstperiodic structure and a second plane including a periodic direction ofthe second periodic structure and a normal to a plane of the secondperiodic structure, the period of the periodic structure in one of thefirst and second planes in which a maximal incident angle of a usedlight beam is larger than that in the other plane is smaller than theperiod of the other periodic structure in the other plane of the firstand second planes.

According to a further aspect of the present invention, in the opticalelement, with respect to a first plane including a periodic direction ofthe first periodic structure and a normal to a plane of the firstperiodic structure and a second plane including a periodic direction ofthe second periodic structure and a normal to a plane of the secondperiodic structure, the period of the periodic structure in one of thefirst and second planes which is closer to parallel to the used lightthan the other plane is smaller than the period of the other periodicstructure in the other plane of the first and second planes.

According to a further aspect of the present invention, in the opticalelement, with defining a representative light beam as a light beam whichis emitted from the optical element and passes through an optical axisof the optical system, with respect to a first plane including aperiodic direction of the first periodic structure and a normal to aplane of the first periodic structure and a second plane including aperiodic direction of the second periodic structure in the opticalelement and a normal to a plane of the first periodic structure, theperiod of the periodic structure in one of the first and second planeswhich is closer to parallel to the representative light beam than theother plane is smaller than the period of the other periodic structurein the other plane of the first and second planes.

According to another aspect of the present invention, an optical devicecomprises an optical element according to claim 14, modulation devicefor modulating light emitted from the optical element based on an imagesignal; and a projection optical system for projecting the lightmodulated by the modulation means to a predetermined plane.

Various modes of the present invention will be disclosed in embodimentsdescribed later.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a structural view showing an optical element according toEmbodiment 1 of the present invention;

FIG. 2 is a schematic view showing a polarization splitting layeraccording to Embodiment 1 of the present invention;

FIGS. 3A, 3B, and 3C are structural views showing the polarizationsplitting layer according to Embodiment 1 of the present invention;

FIGS. 4A, 4B, and 4C are structural views showing a polarizationsplitting layer according to Embodiment 2 of the present invention;

FIGS. 5A, 5B, and 5C are structural views showing a polarizationsplitting layer according to Embodiment 3 of the present invention;

FIGS. 6A, 6B, and 6C are structural views showing a polarizationsplitting layer according to Embodiment 4 of the present invention;

FIG. 7 is a structural view showing a polarization splitting layeraccording to Embodiment 5 of the present invention;

FIG. 8 is a structural view showing a polarization splitting layeraccording to Embodiment 6 of the present invention;

FIG. 9 is a structural view showing a reflection liquid crystalprojector optical system in which a polarization splitting layeraccording to Embodiment 7 of the present invention is incorporated;

FIG. 10A is an explanatory view showing a model of one-dimensional SWSgrating with respect to effective refractive indices;

FIG. 10B is a graph showing changes in effective refractive indicesrelative to a filling factor f of TiO₂ in the one-dimensional SWSgrating shown in FIG. 10A in which a medium of n1 is TiO₂ and a mediumof n2 is air;

FIG. 10C is a graph showing changes in effective refractive indicesrelative to a filling factor f of SiO₂ in the one-dimensional SWSgrating shown in FIG. 10A in which the medium of n1 is SiO₂ and themedium of n2 is air; and

FIG. 10D is a graph showing changes in effective refractive indicesrelative to a filling factor f of ZrO₂ in the one-dimensional SWSgrating shown in FIG. 10A in which the medium of n1 is ZrO₂ and themedium of n2 is air;

FIGS. 11A, 11B, and 11C are graphs showing transmittance of the opticalelement according to Embodiment 1 with respect to P-polarized light andS-polarized light in the cases where incident angles are 35°, 45°, and55° each;

FIGS. 12A, 12B, and 12C are graphs showing transmittance of an opticalelement according to Embodiment 2 with respect to the P-polarized lightand the S-polarized light in the cases where the incident angles are35°, 45°, and 55° each;

FIGS. 13A, 13B, and 13C are graphs showing transmittance of an opticalelement according to Embodiment 3 with respect to the P-polarized lightand the S-polarized light in the cases where the incident angles are35°, 45°, and 55° each;

FIGS. 14A, 14B, and 14C are graphs showing transmittance of an opticalelement according to Embodiment 4 with respect to the P-polarized lightand the S-polarized light in the cases where the incident angles are35°, 45°, and 55° each;

FIG. 15 is a schematic explanatory view showing diffraction caused by agrating;

FIG. 16 is a schematic explanatory view showing directions of apolarization splitting layer according to Embodiment 7 of the presentinvention;

FIG. 17 is a perspective view showing the polarization splitting layeraccording to Embodiment 7 of the present invention;

FIG. 18 is a sectional view showing the polarization splitting layer asviewed from a direction A, according to Embodiment 7 of the presentinvention;

FIG. 19 is a sectional view showing the polarization splitting layer asviewed from a direction B, according to Embodiment 7 of the presentinvention;

FIG. 20 is a schematic view showing a light flux which is made incidenton an optical element according to Embodiment 7 of the presentinvention;

FIG. 21 is a schematic view showing the light flux which is madeincident on the optical element according to Embodiment 7 of the presentinvention;

FIG. 22 is a schematic view showing the light flux which is madeincident on the optical element according to Embodiment 7 of the presentinvention;

FIG. 23 is a schematic view showing the light flux which is madeincident on the optical element according to Embodiment 7 of the presentinvention;

FIG. 24 is a schematic view showing the light flux which is madeincident on the optical element according to Embodiment 7 of the presentinvention;

FIGS. 25A, 25B, and 25C are graphs showing transmittance of the opticalelement according to Embodiment 7 with respect to the P-polarized lightand the S-polarized light in the cases where the incident angles are35°, 45°, and 55° each;

FIG. 26 is a perspective view showing a polarization splitting layeraccording to Embodiment 8 of the present invention;

FIG. 27 is a sectional view showing the polarization splitting layer asviewed from the direction A, according to Embodiment 8 of the presentinvention;

FIG. 28 is a sectional view showing the polarization splitting layer asviewed from the direction B, according to Embodiment 8 of the presentinvention;

FIGS. 29A, 29B, and 29C are graphs showing transmittance of an opticalelement according to Embodiment 8 with respect to the P-polarized lightand the S-polarized light in the cases where the incident angles are35°, 45°, and 55° each;

FIG. 30 is a structural view showing a phase element according toEmbodiment 9 of the present invention;

FIG. 31 is a schematic view showing a light flux which is made incidenton the phase element according to Embodiment 9 of the present invention;

FIG. 32 is a schematic view showing a light flux which is made incidenton the phase element according to Embodiment 9 of the present invention;

FIG. 33 is a schematic view showing a light flux which is made incidenton the phase element according to Embodiment 9 of the present invention;

FIG. 34 is a schematic view showing a light flux which is made incidenton the phase element according to Embodiment 9 of the present invention;

FIG. 35 is a schematic view showing a light flux which is made incidenton the phase element according to Embodiment 9 of the present invention;

FIG. 36 is a schematic view showing a polarization splitting element ofconventional multi-layer film etching type; and

FIG. 37 is a schematic view showing a conventional multi-layer filmpolarization splitting element.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Hereinafter, various preferred embodiments of the present invention willbe described.

First, Embodiment 1 will be described. This embodiment shows an opticalelement in which a plurality of periodic structures each havingstructural birefringence are stacked. Adjacent periodic structures arestacked such that periodic directions thereof are substantiallyorthogonal to each other. Therefore, a polarization splitting element inwhich both a wavelength characteristic and an incident anglecharacteristic are wide and an extinction ratio thereof is high isrealized without a complex structure.

FIG. 1 is a structural view showing a polarization splitting elementaccording to this embodiment (Embodiment 1). FIG. 1 shows a state inwhich a polarization splitting layer 23 composed of a plurality ofperiodic structures each having structural birefringence is sandwichedby two prisms. The polarization splitting layer 23 and the two prismscompose an optical element having a polarization splitting function.

In FIG. 1, the polarization splitting layer 23 is tilted 45° relative toan incident surface 25 of the prism. When an incident light beamincluding a P-polarized light component 18 and an S-polarized lightcomponent 20 is perpendicularly made incident on the incident surface25, the P-polarized light component 18 passes through the polarizationsplitting layer 23 to become passing light 19, and the S-polarized lightcomponent 20 is reflected on the polarization splitting layer 23 tobecome reflective light 21. In this embodiment, the optical element isassumed to be used for visible light.

FIG. 2 is a conceptual view showing the polarization splitting layer 23.The polarization splitting layer 23 has a plurality of gratingstructures (periodic structures) stacked therein. Periodic directions ofadjacent grating structures are substantially orthogonal to each other.In this embodiment, five one-dimensional grating structurescorresponding to five layers are stacked. (FIG. 2 is the conceptualview, so only three one-dimensional grating structures are showntherein. The polarization splitting layer 23 having all the fiveone-dimensional grating structures is shown in FIGS. 3A, 3B, and 3C.)Assume that first, second, third, fourth, and fifth one-dimensionalgratings are arranged in order from a light incident side (upper side ofFIG. 2). A period of each of the grating structures is shorter than awavelength of any incident light. Each of the grating structuresexhibits structural birefringence.

As shown in FIG. 2, an incident surface on which the incident light beam(P-polarized light component 18 and S-polarized light component 20) ismade incident is orthogonal to a periodic direction of the firstone-dimensional grating. The periodic direction of the firstone-dimensional grating is assumed to be a grating direction V. As shownin FIG. 2, a periodic direction of the second one-dimensional grating isorthogonal to the grating direction V and assumed to be a gratingdirection P.

When the light is made incident on the polarization splitting layer 23,the S-polarized light component is reflected thereon and the reflectivelight 21 thereof exits from an exit surface 26 different from theincident surface 25 located on the light incident side of the prism. Atthis time, the P-polarized light component passes through thepolarization splitting layer 23 and the passing light 19 thereof exitsfrom an exit surface 27 located on the light exit side of the prism.

FIG. 3A is an oblique perspective view showing all of the five layers ofthe one-dimensional gratings of the polarization splitting layer 23.FIG. 3B is a sectional view showing the gratings as viewed from adirection A indicated by an arrow 29 in FIG. 2. FIG. 3C is a sectionalview showing the gratings as viewed from a direction B indicated by anarrow 30 in FIG. 2.

Table 1 shows design values related to each of the one-dimensionalgratings of the polarization splitting layer 23 in this embodiment(Embodiment 1). TABLE 1 Embodiment 1 Pitch 0.120 μm Layer Film thicknessFilling Grating number Medium [μm] factor direction 1 TiO₂ 0.073 0.70 V2 TiO₂ 0.231 0.30 P 3 TiO₂ 0.076 0.70 V 4 TiO₂ 0.231 0.30 P 5 TiO₂ 0.0730.70 VPrism medium n_(p) = 1.603

A material of each of the one-dimensional gratings is a titanium oxideTiO₂ which is a dielectric. Each of the one-dimensional gratings has astructure in which a dielectric and air are periodically alternatelyrepeated. In this embodiment, the polarization splitting is realizedusing a relatively simple structure having five layers in total. Here,each of first, third, and fifth one-dimensional gratings 101, 103, and105 is referred to as a layer H and each of second and fourthone-dimensional gratings 102 and 104 is referred to as a layer L. When arefractive index of a material of each of the one-dimensional gratingsis given by n1, it is preferable to satisfy the following conditionalexpression (7).1.5<ni  (7)

The layer H and the layer L corresponding to the respective layersrespectively exhibit high and low effective refractive indices withrespect to the S-polarized light to be reflected. A thickness of thelayer H is 73 nm to 76 nm and sufficiently satisfies the followingconditional expression (8).(n1s·d ₁·cos θ)/λ_(s)<0.5  (8)Here, n1s and d₁ denote an effective refractive index of each of thelayers H with respect to the S-polarized light and a thickness thereof,respectively. In addition, θ denotes an incident angle. In thisembodiment, θ=45°. λ_(s) denotes a wavelength of the incident lighthaving a minimal wavelength. The optical element according to thisembodiment is assumed to be used for the visible light. Therefore, theincident light is the visible light (400 nm to 700 nm) and λ_(s) is 400nm which is the minimal wavelength of those.

The conditional expression (8) completely achieves the reflection of theS-polarized light. In general, there has been known that the incidentlight is totally reflected without any passing in the case where anincident angle when light is made incident on a low refractive indexmedium from a high refractive index medium is equal to or larger than acritical angle θ_(c). However, in this time, evanescent light seepsthrough an extremely small region near an interface surface. Whenanother medium exists in a region which the light reaches, the lightpasses therethrough. Such a phenomenon is attenuated total reflection(ATR). The conditional expression (8) is used to obtain a highreflectance over a wide-angle range and a wide-wavelength range based onthe interference of ATR lights with one another. When (n1s·d₁·cosθ)/λ_(s) exceeds the upper limit of the conditional expression (8), thatis, when the film thickness set in view of the incident angle becomes ½of the wavelength, reflective light beams in ATR interferes with oneanother, thereby reducing the reflectance. When the film thicknesschanges, a reduction in reflectance due to the interference is causedevery ½ change in wavelength. The conditional expression (8) is used toprevent the interference from occurring over a wide used wavelengthrange.

The layer L satisfies the following conditional expression (9). Theconditional expression (9) is used to effectively utilize the reflectionrelated to ATR.0.2<d ₂/λ_(s)<1.0  (9)Here, d₂ denote a thickness of the layer L, which is 231 nm.

When the film thickness is decreased so that d₂/λ_(s) becomes lower thanthe lower limit of the conditional expression (9), the transmittance ofthe ATP increases in an incident angle range equal to or larger than thecritical angle. Therefore, sufficient reflection cannot be realized.

In view of the ATR, it is preferable to maximize the film thickness.However, even when the film thickness increases, the reflectanceasymptotically approaches the total reflection, so that an effectcorresponding to an increase in film thickness cannot be obtained. Inthe one-dimensional grating shape, the difficulty of manufacturingincreases as the film thickness increases. Therefore, it is preferableto set the film thickness to the upper limit of the conditionalexpression (9).

A used angle range includes an angle which is equal to or smaller thanthe critical angle and at which normal reflection is caused. When thefilm thickness is set such that d₂/λ_(s) becomes smaller than the upperlimit of the conditional expression (9), a suitable result is obtainedwith respect to the interference due to the normal reflection.

In Embodiment 1, a glass material having a relatively low refractiveindex of about 1.603 is used for the prisms sandwiching the polarizationsplitting layer 23. An absolute value of a photoelastic coefficient ofthe prism is smaller than 0.1×10⁻⁸ cm²/N. Each of a dielectric of thelayer H corresponding to the one-dimensional grating in the gratingdirection V and a dielectric of the layer L corresponding to theone-dimensional grating in the grating direction P is TiO₂ and has ahigh refractive index of 2.282. In order to efficiently produce abirefringence, a filling factor f1 of the layer H is set in the range ofthe conditional expression (10) and a filling factor f2 of the layer Lis set in the range of the conditional expression (11). The fillingfactor in this embodiment is also the ratio of a TiO₂ width to a pitch.0.3<f1<1.0  (10)0.10<f2<0.5  (11)

The conditional expressions (10) and (11) express conditions toefficiently produce structural birefringence. As shown in the graph ofFIG. 10B, a large difference between the effective refractive indices ofTE and TM causes large birefringence. In each of the cases of f=0 andf=1, the difference of refractive index to a medium becomes 0. In thecase where f is about 0.5, the difference is maximum. Therefore, whenthe filling factors are set in the ranges of the conditional expressions(10) and (11), it is possible to efficiently use the effectiverefractive indices.

More preferably, the filling factors f1 and f2 satisfy the respectivefollowing conditional expressions (10a) and (11a),0.65<f1<0.95  (10a),0.2<f2<0.45  (11a).

The effective refractive indices of the layer H and layer L that exhibitthe structural birefringence are expressed by the expressions (4) and(5) described earlier. Here, TM corresponds to a polarized lightcomponent in a direction parallel to the periodic direction of a gratingand TE corresponds to a polarized light component in a directionorthogonal to the periodic direction of the grating. With respect to thelayer corresponding to the one-dimensional grating in the gratingdirection V, the P-polarized light becomes TM and the S-polarized lightbecomes TE. With respect to the layer corresponding to theone-dimensional grating in the grating direction P, the P-polarizedlight becomes TE and the S-polarized light becomes TM.

FIG. 10B is a graph showing the effective refractive indices related tothe respective polarized light when the filling factor f (ratio of TiO₂width to pitch) is changed in the case where one of mediums is TiO₂ andthe other is air in the expressions (4) and (5).

As shown in Table 2, with respect to the P-polarized light, in the caseof f=0.7 in the first one-dimensional grating, the effective refractiveindex in the TM direction becomes 1.60. In the case of f=0.3 in thesecond one-dimensional grating, the effective refractive index in the TEdirection becomes 1.57. In other words, a difference between theeffective refractive indices of the respective layers is small withrespect to the P-polarized light and the effective refractive indicesare close to the refractive index of the prism medium. Therefore, thereflection can be suppressed to obtain a high transmittance. In order toincrease the transmittance with respect to the P-polarized light, it ispreferable to satisfy the following conditional expression (12).0.95<n1p/n2p<1.2  (12)

When n1p/n2p exceeds the upper limit of the conditional expression (12)or becomes smaller than the lower limit thereof, a difference betweenthe effective refractive indices of the one-dimensional gratings withrespect to the P-polarized light becomes larger. Therefore, thereflectance increases and the transmittance reduces. Table 2 showseffective refractive indices n_(p) and n_(s) of the respectiveone-dimensional gratings with respect to the P-polarized light and theS-polarized light, and values in the expressions (8) and (9). TABLE 2Embodiment 1 Values in conditional expressions Layer number n_(p) n_(s)(8) (9) 1 1.60 2.05 0.265 — 2 1.57 1.16 — 0.578 3 1.60 2.05 0.275 — 41.57 1.16 — 0.578 5 1.60 2.05 0.265 —θ = 45°,λs = 400 nm

When n_(H)=1.60, n_(L)=1.57, and n_(p)=1.603 are substituted into theexpression (2), the Brewster's angle θ_(B) becomes about 44.3°.Therefore, the configuration satisfies a condition in which an incidentlight flux with an incident angle of 45° is substantially completelytransmitted.

As shown in Table 2, with respect to the S-polarized light, in the caseof the first one-dimensional grating, the effective refractive index inthe TE direction becomes 2.05. In the case of the second one-dimensionalgrating, the effective refractive index in the TM direction becomes1.16. When n₁=1.603 and n₂=1.16 are substituted into the expression (3),the critical angle θ_(C) becomes about 46°. Therefore, the reflectionrelated to the ATR is caused at a higher incident angle than thecritical angle θ_(C). The normal reflection on a dielectric interface iscaused even on a low incident angle side. However, the incident angle isclose to the critical angle and a difference between the refractiveindices (2.05 and 1.16) is large. Thus, high reflectance is obtained ineach interface.

As described above, with respect to the P-polarized light, the effectiverefractive indices of the one-dimensional gratings in the gratingdirections V and P become close to each other. With respect to theS-polarized light, the difference between the refractive indices becomeslarge. Therefore, the transmission and reflection of each of thepolarized light beams are realized.

A relationship between the effective refractive indices of theone-dimensional gratings in the grating directions V and P can beefficiently realized by satisfying the following conditional expressions(12), (13), and (14).n1p<n1s  (12)n2p>n2s  (13)|n1s−n2s|>|n1p−n2p|  (14)

FIGS. 11A, 11B, and 11C show transmittance characteristic obtained by asimulation based on rigorous coupled-wave analysis (RCWA) using thedesign values. In each of FIGS. 11A, 11B, and 11C, the abscissa axisindicates a wavelength and the ordinate axis indicates the transmittancewith respect to the P-polarized light and the S-polarized light. FIG.11A shows the case where the incident angle is 35°. FIG. 11B shows thecase where the incident angle is 45°. FIG. 11C shows the case where theincident angle is 55°. With respect to the P-polarized light, thetransmittance lowers at the high incident angle. However, the loweredtransmittance is a level that there is substantially no problem inpractical use.

With respect to the S-polarized light, although the performancedeteriorates on a short wavelength side of a low incident angle, thereare little light beams passing through the polarization splitting layerin a very wide incident angle range of 35° to 55°, that is, completereflectance is achieved.

In the embodiment 1, the polarizing direction of the light to bereflected (S-polarized light beam) is substantially parallel to eitherof the directions of the periodic structures whose periodic directionsare perpendicular to each other (preferably the angle between thedirections is not greater than 5 degrees). The characteristic of thepolarization splitting improves by such a configuration.

Subsequently, other embodiments of the present invention will bedescribed.

In each of Embodiments 2 to 4 described below, the polarizationsplitting layer 23 composed of periodic structures having structuralbirefringence is sandwiched by two prisms. This is identical to that ofEmbodiment 1. A schematic structure is the same as that of FIG. 1. Arelationship between the incident light and the exit light issubstantially identical to that of Embodiment 1. A structure of thepolarization splitting layer 23 in each of Embodiments 2 to 4 isdifferent from that of Embodiment 1. Hereinafter, Embodiments 2 to 4will be described in order.

Table 3 shows design values related to a structure in Embodiment 2. Inthis embodiment, the number of stacked layers of one-dimensionalgratings is three. TABLE 3 Embodiment 2 Pitch 0.120 μm Layer Filmthickness Filling Grating number Medium [μm] factor direction 1 TiO₂0.351 0.22 P 2 TiO₂ 0.066 0.85 V 3 TiO₂ 0.351 0.22 PPrism medium n_(p) = 1.603

FIG. 4A is an oblique structural view showing gratings in Embodiment 2.FIG. 4B is a sectional structural view showing the gratings as viewedfrom the direction A indicated by the arrow 29 in FIG. 2. FIG. 4C is asectional structural view showing the gratings as viewed from thedirection B indicated by the arrow 30 in FIG. 2. Each of theone-dimensional gratings has a structure in which air and TiO₂ arealternately repeated. Table 4 shows the values in the conditionalexpressions (8) and (9). TABLE 4 Embodiment 2 Values in conditionalexpressions Layer number n_(p) n_(s) (8) (9) 1 1.71 1.24 — 0.878 2 1.602.05 0.285 — 3 1.71 1.24 — 0.878θ = 45°,λs = 400 nm

As is apparent from Table 2, the conditional expressions (8) and (9) aresatisfied in Embodiment 2. In addition, the conditional expressions (10)and (11) are satisfied. In this embodiment, the respectiveone-dimensional gratings are suitably set to realize the polarizationsplitting layer using a simple structure having three layers in total.

FIGS. 12A, 12B, and 12C show transmittance characteristics obtained by asimulation based on RCWA calculation in Embodiment 2. The reflection ofthe S-polarized light deteriorates at the low incident angle. TheS-polarized light passes through the polarization splitting layer in allwavelengths, however, sufficient reflectance is obtained at each of theincident angles of 45° and 55°. With respect to the P-polarized light,sufficient transmittance is obtained over the entire angle range and theentire wavelength range, with the result that a preferable performanceis realized.

Subsequently, Embodiment 3 will be described. Table 5 shows the designvalues in Embodiment 3. FIGS. 5A, 5B, and 5C show an outer shape andsectional shapes. TABLE 5 Embodiment 3 Pitch 0.120 μm Layer Filmthickness Filling Grating number Medium [μm] factor direction 1 TiO₂0.073 0.90 V 2 TiO₂ 0.231 0.30 P 3 TiO₂ 0.076 0.90 V 4 TiO₂ 0.231 0.30 P5 TiO₂ 0.073 0.90 VPrism medium n_(p) = 1.603

The conditional expressions (8) and (9) are satisfied as shown in Table6. In addition, conditional expressions (10) and (11) are satisfied.TABLE 6 Embodiment 3 Values in conditional expressions Layer numbern_(p) n_(s) (8) (9) 1 1.99 2.23 0.288 — 2 1.57 1.16 — 0.578 3 1.99 2.230.300 — 4 1.57 1.16 — 0.578 5 1.99 2.23 0.288 —θ = 45°,λs = 400 nm

FIGS. 13A, 13B, and 13C show transmittance characteristics obtained by asimulation based on RCWA calculation in Embodiment 3. The reflectancerelated to the S-polarized light on a short wavelength side reduces atthe low incident angle. On the other hand, the transmittance related tothe P-polarized light is improved, so that the entire performance ispreferable.

Subsequently, Embodiment 4 will be described. Table 7 shows the designvalues in Embodiment 4. FIGS. 6A, 6B, and 6C show an outer shape andsectional shapes. TABLE 7 Embodiment 4 Pitch 0.120 μm Layer Filmthickness Filling Grating number Medium [μm] factor direction 1 TiO₂0.073 0.90 V 2 ZrO₂ 0.182 0.30 P 3 TiO₂ 0.075 0.90 V 4 ZrO₂ 0.182 0.30 P5 TiO₂ 0.073 0.90 VPrism medium n_(p) = 1.603

The conditional expressions (8) and (9) are satisfied as shown in Table8. In addition, conditional expressions (10) and (11) are satisfied.TABLE 8 Embodiment 4 Values in conditional expressions Layer numbern_(p) n_(s) (8) (9) 1 1.99 2.23 0.288 — 2 1.42 1.15 — 0.455 3 1.99 2.230.296 — 4 1.42 1.15 — 0.455 5 1.99 2.23 0.288 —θ = 45°,λs = 400 nm

FIGS. 14A, 14B, and 14C show transmittance characteristics obtained by asimulation based on RCWA calculation in Embodiment 4. A five-layerstructure is used. A dielectric for the second one-dimensional gratingcorresponding to the layer L is ZrO₂. When the filling factor f is 0.3,substantially the same birefringence as that of TiO₂ is obtained. Thetransmittance related to the P-polarized light reduces at the lowincident angle and the high incident angle. On the other hand, withrespect to the S-polarized light, preferable reflectance is obtained atall incident angles and over the entire wavelength range.

Subsequently, Embodiment 5 of the present invention will be described.FIG. 7 is a structural view showing an optical element according toEmbodiment 5. Although the rectangular prism is used in each ofEmbodiments 1 to 4, a prism deformed in a rhombic shape is used in thisembodiment. In Embodiment 5, the same polarization splitting layer asdescribed in any one of Embodiments 1 to 4 is sandwiched by two prismsdeformed in the rhombic shape. In FIG. 7, the incident light beams 18and 20 from the left are perpendicularly made incident on a prismsurface and then made incident on the polarization splitting layer at anangle larger than 45°. The total reflection on the polarizationsplitting layer becomes easier as the incident angle increases.Therefore, the prism is deformed in the rhombic shape at a tilt of about10° to obtain the incident angle larger than that in the rectangularprism by 5°. Thus, the reflectance with respect to the S-polarized lightcan be increased.

Subsequently, Embodiment 6 of the present invention will be described.FIG. 8 is a structural view showing an optical element according toEmbodiment 6. The same polarization splitting layer as described in anyone of Embodiments 1 to 4 is sandwiched by plates made of substantiallythe same material as that of the prism and the resultant is additionallysandwiched by triangular prisms. The polarization splitting layer thatrequires micro-machining is sandwiched by glass plates to construct asingle unit. Therefore, the prisms that require shape performances suchas angles, sizes, and profile irregularities are separated from eachother to improve productivity.

Subsequently, Embodiment 7 of the present invention will be described.In each of the optical elements described in the embodiments up to here,the pitches (periods) of the one-dimensional gratings composing thepolarization splitting layer are equal to one another. On the otherhand, in this embodiment, the pitches of the plurality ofone-dimensional gratings composing the polarization splitting layer aremade different from one another. In particular, when the pitches aresuitably set according to the incident angles of incident light and theincident directions thereof, the polarization splitting layer which iseasily produced is provided while desirable performance is realized.

As described above, when the period of the one-dimensional grating ismade equal to or shorter than the wavelength of the incident light, thegrating exhibits the birefringent characteristic relative to theincident light, and the refractive index thereof can be given as theeffective refractive index.

A condition in which the refractive index of the one-dimensional gratingcan be given as the effective refractive index is a condition in whichthe pitch of the grating is sufficiently small and the diffraction ofthe incident light does not occur.

As shown in FIG. 15, assume that a refractive index of a light incidentside medium of a grating having a pitch d is given by n1, a refractiveindex of a light exit side medium thereof is given by n2, an incidentangle of the incident light is given by θ1, and an exit angle of theexit light caused by diffraction is given by θ2. Here, when an opticalpath difference (L1−L2) between adjacent light beams becomes an integralmultiple of the wavelength, diffraction light is produced. This isexpressed by the following expression (15). When this expression issatisfied, the diffraction occurs,dn1 sin θ1−dn2 sin θ2=mλ  (15),where m is an integer.

When the expression (15) doesn't have any solution except m=0, thediffraction does not occur.

Each of the refractive indices of the light incident side medium and thelight exit side medium is set to n and the expression (15) is modifiedto the expression (16).sin θ1−sin θ2=mλ/dn  (16)

When θ1 and θ2 take arbitrary values, the left side of the expression(16) becomes a range expressed by the expression (17).−2≦sin θ1−sin θ2≦2  (17)

Therefore, when λ/dn is larger than the left side, the diffraction doesnot occur. That is, the expression (18) is a condition for preventingthe diffraction from occurring at all incident angles.d<λ/2n  (18)

However, when an element satisfying the above-mentioned condition issandwiched between the two prisms (prism portions) as in the case of thepolarization splitting layer, the refractive index n in the conditionalexpression (18) becomes larger than that of air. Therefore, a pitch forpreventing diffraction from occurring narrows. In the above-mentionedone-dimensional grating, when the pitch is narrowed without changes infilling factor and thickness h of the grating, a ratio between a heightof the grating and a width thereof (aspect ratio) becomes larger,leading to an increase in the difficulty of manufacturing.

In this embodiment, the pitches are suitably set according to theincident angle of a used light flux and the direction thereof, so thatthe optical element which is easily manufactured is realized while thecondition on which diffraction is prevented from occurring with respectto all light fluxes is maintained.

The optical element according to Embodiment 7 has the stricture in whichthe polarization splitting layer 23 is sandwiched by the prisms as shownin FIG. 1. Table 9 shows values related to the structure of thepolarization splitting layer 23 of Embodiment 7.

Although the visible light band range is defined as the wavelength inuse in the embodiments described above, the wavelength band range in usemay be defined the range of 450 nm to 700 nm in which the difference intransmittance between S-polarized light and P-polarized light is notless than 70%. Since the difference in transmittance between S-polarizedlight and P-polarized light is not less than 80% in a wavelength bandrange of 480 nm to 650 nm, the excellent characteristic as apolarization splitting element (polarization beam splitter) is proved.On the other hand, the period of the periodic structure in thisembodiment is to be configured preferably not greater than 400 nm, morepreferably, not greater than 350 nm. Off course, the structure having aperiodic structure can contain a layer which has a function other thanpolarization splitting function and whose period is greater than 400 nm.TABLE 9 Embodiment 7 Layer Film thickness Grating Pitch F(Filling Mediumwidth Air thickness number Medium [μm] direction p[nm] factor) a[nm]b[nm] 1 TiO2 370 P 200 0.18 36 164 2 TiO2 64 V 140 0.84 118 22 3 TiO2370 P 200 0.18 36 164Prism medium n_(p) = 1.603

As in Embodiment 1, the polarization splitting layer 23 is tilted 45°with respect to the incident surface 25 of the prism as shown in FIG. 1.The P-polarized light 18 and the S-polarized light 20 of the incidentlight beam which is perpendicularly made incident on the incidentsurface 25 are made incident on the polarization splitting layer 23. TheS-polarized light is reflected on the polarization splitting layer 23 tobecome the reflective light 21. The reflective light 21 exits from theexit surface 26 different from the incident surface 25 of a prism 22located on the light incident side as shown in FIG. 1. The P-polarizedlight passes through the polarization splitting layer 23 to become thepassing light 19. The passing light 19 exits from the exit surface 27 ofa prism 24 located on the light exit side.

FIG. 16 is a schematic view showing grating directions. As shown in FIG.2, an incident plane 28 within which light is made incident on thepolarization splitting layer 23 and the first one-dimensional grating ofthe polarization splitting layer 23 are parallel to each other and theparallel direction is assumed to be the grating direction P. As shown inFIG. 2, the second one-dimensional grating is located perpendicular tothe incident plane 28, and the perpendicular direction is assumed to bethe grating direction V.

FIG. 17 is an oblique perspective view showing the polarizationsplitting layer 23. FIG. 18 is a sectional structural view showing thegratings as viewed from the direction A indicated by the arrow 29 inFIG. 16. FIG. 19 is a sectional structural view showing the gratings asviewed from the direction B indicated by the arrow 30 in FIG. 16. Thefirst and third one-dimensional gratings 101 and 103 are of the layer Lhaving the grating direction P in which air and a dielectric arealternately repeated. The second one-dimensional grating 102 is of thelayer H having the grating direction V in which the air and thedielectric are alternately repeated. The polarization splitting can berealized using a relatively simple structure having three layers intotal. TiO₂ is used as the dielectric.

In Embodiment 7, as is apparent from the design values in Table 9, aglass material having a relatively low refractive index of about 1.603is used for the prism. In order to efficiently produce birefringence,each of a dielectric of the layer H which is the one-dimensional gratinghaving the grating direction V and a dielectric of the layer L which isthe one-dimensional grating having the grating direction P is made ofTiO₂ having a high refractive index of 2.282, and the filling factor ofthe layer L is set to 0.18 and the filling factor of the layer H is setto 0.84.

FIG. 20 shows an incident light beam. As shown in FIG. 20, the incidentlight beam is made incident on the prism as a convergent light beam 31(FNo. is about 2.0) having a circular opening about an optical axis 32formed at 45° relative to the polarization splitting layer. Here, asshown in FIG. 21, when a plane including the periodic direction of thegrating in the grating direction P and the optical axis 32 is assumed tobe a cross section 33, an angle of the incident light beam within thecross section 33 is shown in FIG. 22 and its width is θ3 about theoptical axis.

As shown in FIG. 23, when a plane including the periodic direction ofthe grating in the grating direction V and the optical axis 32 isassumed to be a cross section 34, an angle of the incident light beamwithin the cross section 34 is shown in FIG. 24. That is, the opticalaxis is tilted θ0, so a maximal incident angle of the light beam is θ3.

It is necessary that the incident angle of the light beam within each ofthe cross sections and the grating pitch should be in a relationship inwhich diffraction is prevented from occurring. In the cross sectionshown in FIG. 22, the incident angle θ0 of the light beam on the opticalaxis relative to the grating is 0°. The maximal incident angle θ3 of thelight beam is about 14.5° in the case where FNo. is 2.0.

Here, in the above-mentioned conditional expression (16) related to thediffraction;sin θ1−sin θ2=mλ/dn  (16),the incident angle θ1 of the incident light is within the followingrange (19) and sin θ1 is within the following range (20).−14.5≦θ1≦14.5  (19)−0.25≦sin θ1≦0.25  (20)

When θ2 is an arbitrary value, an assumable value for the left side ofthe expression (17) falls within the following range.−1.25≦sin θ1−sin θ2≦1.25  (21)

Therefore, when the following conditional expression (22) is satisfied,solution to the expression (16) is only m=0.1.25<λ/dn  (22)

That is, when the pitch d of the grating satisfies the followingconditional expression (23), the diffraction does not occur.d<λ/1.25n  (23)

When a shortest wavelength λ (=430 nm) of used wavelengths in thisembodiment, and a refraction index n (=1.603) of the prism aresubstituted into the conditional expression (23), the following resultis obtained.d<215 [nm]  (24)

The grating pitch shown in the sectional view of FIG. 22, that is, thegrating pitch of the layer L becomes 200 nm which is a valuesubstantially satisfying the above-mentioned condition as shown in Table9.

In the cross section shown in FIG. 24, the incident angle θ0 of thelight beam on the optical axis relative to the grating is 45°, and themaximal incident angle θ3 of the light beam is about 59.5°. When thosevalues are treated in a similar manner as described above, when θ2 is anarbitrary value, an assumable value for the left side of the expression(16) falls within a range of the following expression (25). When thegrating pitch d satisfies the following conditional expression (26), thediffraction does not occur.−1.87≦sin θ1−sin θ2≦1.87  (25)d<λ/1.87n  (26)

When a shortest wavelength λ (=430 nm) of used wavelengths, and arefraction index n (=1.603) of the prism are substituted into theconditional expression (26), the following result is obtained.d<143 [nm]  (27)

The grating pitch shown in the sectional view of FIG. 24, that is, thegrating pitch of the layer H is 140 nm which is a value substantiallysatisfying the above-mentioned condition as shown in Table 9.

With respect to the incident angle θ0 of the light beam on the opticalaxis and the maximal incident angle θ3 of the light beam, a direction inwhich the incident angles θ0 and θ3 become maximal is in the case wherethe incident plane is in the direction V. Therefore, when a pitch ofeach of the gratings 101 and 103 of the layers L is given by P_(B) and apitch of the grating 102 of the layer H is given by P_(A), valuessatisfying the following conditional expression (28) are set.P_(A)<P_(B)  (28)

As shown in Table 9, the pitch of the grating of the layer L is largerthan the pitch of the grating of the layer H. In the grating of thelayer L, a medium width rate is small and the layer is thick, so anaspect ratio (ratio of a grating thickness to a grating width) islarger. When the pitch is made larger as much as possible, the aspectratio is reduced to lower the degree of difficulty in manufacturing.

As described above, the optical element (polarization splitting element)in this embodiment can be defined as follows. The optical element inthis embodiment includes a first periodic structure having a periodsmaller than the wavelength of used light (in this embodiment, lightwithin the visible light band range of 400 to 700 nm, more preferably,450 to 650 nm) and a second periodic structure which has a periodsmaller than the wavelength of the used light and in which the directionof the second periodic structure is perpendicular or substantiallyperpendicular to the that of the first periodic structure. In thisembodiment, the first periodic structure and the second periodicstructure are adjacent to each other.

The optical element according to this embodiment is an optical elementas described above and has the following features. With respect to afirst plane including a periodic direction of the first periodicstructure and a normal to the plane of the first periodic structure(either the plane shown in FIG. 22 or the plane shown in FIG. 24) and asecond plane including a periodic direction of the second periodicstructure and a normal to the plane of the second periodic structure(the other plane, which is not the first plane, of the plane shown inFIG. 22 and the plane shown in FIG. 24), the period of the periodicstructure in one of the first and second planes in which a maximalincident angle of a used light beam is larger than that in the otherplane is smaller than the period of the other periodic structure in theother plane of the first and second planes.

Further, the feature of the optical element according to this embodimentcan be described as follows. With respect to a first plane including aperiodic direction of the first periodic structure and a normal to theplane of the first periodic structure (either the plane shown in FIG. 22or the plane shown in FIG. 24) and a second plane including a periodicdirection of the second periodic structure and a normal to the plane ofthe second periodic structure (the other plane, which is not the firstplane, of the plane shown in FIG. 22 and the plane shown in FIG. 24),the period of the periodic structure in one of the first and secondplanes which is closer to parallel to the used light than the otherplane (a plane shown in FIG. 24) is smaller than the period of the otherperiodic structure in the other plane of the first and second planes.

Furthermore, the feature of the optical element according to thisembodiment can also be described as follows. Assuming that arepresentative light beam be a light beam emitted from the opticalelement and passing through an optical axis of an optical element in thelatter part, with respect to a first plane including a periodicdirection of the first periodic structure and a normal to the plane ofthe first periodic structure (either the plane shown in FIG. 22 or theplane shown in FIG. 24) and a second plane including a periodicdirection of the second periodic structure and a normal to the plane ofthe second periodic structure (the other plane, which is not the firstplane, of the plane shown in FIG. 22 and the plane shown in FIG. 24),the period of the periodic structure in one of the first and secondplanes which is closer to parallel to the representative light beam thanthe other plane (a plane shown in FIG. 24) is smaller than the period ofthe other periodic structure in the other plane of the first and secondplanes.

In this embodiment, the two periodic structures are orthogonal to eachother. Of the light incident plane including a periodic direction of oneof the periodic structures with respect to the incident light and thelight incident plane including a periodic direction of the other of theperiodic structures, the period of a periodic structure within anincident plane in which the maximal incident angle of a light beam islarger than the other is made to be smaller than the period of aperiodic structure within the other incident plane.

Instead of the maximal incident angle of a light beam, the incidentangle of the central light beam (light beam 32 in FIG. 21) may be used.With respect to the incident angle of the central light beam (light beam32 in FIG. 21), of the light incident plane including the periodicdirection of one of the periodic structures and the light incident planeincluding the periodic direction of the other of the periodicstructures, the period of a periodic structure within an incident planein which the incident angle of the central light beam is larger than theother is to be smaller than the period of a periodic structure withinthe other incident plane.

When light exited from the optical element according to this embodimentis made incident on another optical system, a light beam passing throughthe optical axis of the optical system is used as a representative lightbeam. With respect to the representative light beam, of the lightincident plane including the periodic direction of one of the periodicstructures and the light incident plane including the periodic directionof the other of the periodic structures, the period of a periodicstructure within an incident plane in which the incident angle of therepresentative light beam is larger than the other may be to be smallerthan the period of a periodic structure within the other incident plane.

FIGS. 25A, 25B, and 25C show transmittance characteristics obtained by asimulation based on RCWA in Embodiment 7. With respect to theP-polarized light, the transmittance lowers at the high incident angle.However, the lowered transmittance is a level at which substantially noproblem is caused in practical use.

With respect to the S-polarized light, the complete reflectance isachieved, because there are little light beams passing through thepolarization splitting layer in a very wide incident angle range of 35°to 55° except for that the performance on a short wavelength sidedeteriorates at a low incident angle.

Subsequently, Embodiment 8 of the present invention will be described.In Embodiment 7, the three one-dimensional gratings corresponding thethree layers are stacked. In this embodiment, the five one-dimensionalgratings corresponding the five layers are stacked.

FIG. 26 shows a structure of a polarization splitting layer. FIG. 22 isan oblique perspective view showing gratings. FIGS. 27 and 28 aresectional views showing one-dimensional gratings 201 to 205 ofpolarization splitting layer as viewed from the directions shown in FIG.16 as in Embodiment 7.

Each of the one-dimensional gratings 201, 203, and 205 of the layer H inthe grating direction V in which air and a dielectric are alternatelyrepeated. Each of the one-dimensional grating 202 and 204 of the layer Lin the grating direction P in which the air and the dielectric arealternately repeated.

The polarization splitting is realized using a relatively simplestructure having five layers in total. TiO₂ is used as the dielectric.

In Embodiment 8, as is apparent from the design values in Table 10, aglass material having a relatively low refractive index of about 1.603is used for the prism. Each of the layer H corresponding to theone-dimensional grating in the grating direction V and the layer Lcorresponding to the one-dimensional grating in the grating direction Pinclude TiO₂ a dielectric having a high refractive index of 2.282. Inorder to efficiently produce birefringence, the filling factor of thelayer L is set to 0.30 and the filling factor of the layer H is set to0.90. TABLE 10 Embodiment 8 Layer Film thickness Grating Pitch f(FillingMedium width Air width number Medium [μm] direction p[nm] factor) a[nm]b[nm] 1 TiO2 73 V 120 0.9 270 30 2 TiO2 231 P 300 0.3 90 210 3 TiO2 76 V120 0.9 270 30 4 TiO2 231 P 300 0.3 90 210 5 TiO2 73 V 120 0.9 270 30Prism medium n_(p) = 1.603

As shown in Table 10, with respect to the P-polarized light, in the caseof f=0.30 in the first one-dimensional grating, the effective refractiveindex in the TE direction is 1.55. In the case of f=0.90 in the secondone-dimensional grating, the effective refractive index in the TMdirection is 1.98.

On the other hand, as shown in Table 10, with respect to the S-polarizedlight, in the case of the first one-dimensional grating, the effectiverefractive index in the TM direction is 1.55. In the case of the secondone-dimensional grating, the effective refractive index in the TEdirection is 2.21.

Therefore, with respect to the P-polarized light, the effectiverefractive indices of the first and second one-dimensional gratings areclose to each other. With respect to the S-polarized light, thedifference between the refractive indices is made large, therebyrealizing the transmission and reflection of each of polarized lightbeams.

With respect to the incident light beam, this embodiment is identical toEmbodiment 7.

In FIGS. 22 and 24, it is necessary that the incident angle of the lightbeam within each of the cross sections 33 and 34 and the grating pitchshould be in a relationship in which diffraction is prevented fromoccurring. Pitch conditions of the respective gratings at this time areexpressed by the expressions (24) and (27).

As shown in Table 10, the pitch of the grating of the layer H is 120 nmand satisfies the conditional expression (27). On the other hand, thepitch of the grating of the layer L is 300 nm and does not satisfy theconditional expression (24). However, the pitch of the grating of thelayer L widens up to be within the bounds of not causing substantialproblem in performance.

With respect to the incident angle θ0 of the light beam on the opticalaxis and the maximal incident angle θ3 of the light beam, a direction inwhich the incident angles becomes maximal is in the case where theincident plane is in the direction V. Therefore, when a pitch of each ofthe gratings 202 and 204 of the layers L is given by P_(B) and a pitchof each of the gratings 201, 203, and 205 of the layers H is given byP_(A), which satisfy the conditional expression (28).

As shown in Table 10, the pitch of the grating of the layer L is largerthan the pitch of the grating of the layer H. In the grating of thelayer L, the medium width is small relative to that of air and the layeris thick, so the aspect ratio (ratio of the grating thickness to thegrating width) is large. When the pitch is made larger as much aspossible, the aspect ratio is reduced to lower the degree of difficultyin manufacturing.

FIGS. 29A, 29B, and 29C show transmittance characteristics obtained by asimulation based on RCWA in Embodiment 8. With respect to theP-polarized light, the transmittance slightly lowers at the low incidentangle. However, substantially preferable performance is achieved atangles other than the low incident angle.

With respect to the S-polarized light, the complete reflectance isachieved, because there are little light beams passing through thepolarization splitting layer in a very wide incident angle range of 35°to 55° except for that the performance on a short wavelength sidedeteriorates at the low incident angle.

Subsequently, Embodiment 9 of the present invention will be described.The incident angle of the incident light in Embodiment 9 is differentfrom those in Embodiments 7 and 8.

FIG. 30 shows a polarization splitting layer in Embodiment 9. An opticaldevice according to Embodiment 9 is a device, such as a phase plate,used for a structure on which light is incident at an incident angle of0°. As shown in FIG. 30, one-dimensional gratings 35 and 36 are stackedsuch that they are orthogonal to each other. FIG. 31 shows the incidentlight beam in Embodiment 9. As shown in FIG. 31, the light beam on theoptical axis 32 is made incident on the polarization splitting layer atthe incident angle of 0° and has an elliptical opening about the opticalaxis 32. A light beam on a sectional view 37 including the major axis ofthe elliptical opening as shown in FIG. 32 is a light beam as shown inFIG. 34. In addition, a light beam on a sectional view 38 including theminor axis of the elliptical opening as shown in FIG. 33 is a light beamas shown in FIG. 35.

The incident light beam on the cross section 37 shown in FIG. 34 has anopening with FNo.=2.0 and θ4 is 14.5°. Therefore, as in Embodiment 7, itis necessary that the grating pitch in the cross sectional directionsatisfy the expression (24).d<215 [nm]  (24)

On the other hand, the incident light beam on the cross section 38 shownin FIG. 35 has an opening with FNo.=4.0 and θ5 is 7.2. The grating pitchin the cross sectional direction is expressed by the expression (29)based on the same calculation.d<238 [nm]  (29)

The pitches of the respective gratings satisfy the conditionalexpressions (24) and (29), so the diffraction does not occur.

In Embodiment 9, the light beam in which the cross section 37 shown inFIG. 34 is the incident plane has the maximal incident angle. Therefore,a grating pitch shown in FIG. 34 is P_(A) and a grating pitch orthogonalto the grating pitch is P_(B). As shown in Table 11, values of thosegrating pitches satisfies the conditional expression (28).

Table 11 shows values of P_(A) and P_(B) in each of Embodiments 7 to 9.TABLE 11 P_(A), P_(B) in Embodiments 7-9 P_(A) P_(B) Embodiment 7 140200 Embodiment 8 120 300 Embodiment 9 200 230

Finally, Embodiment 10 of the present invention will be described.Embodiment 10 shows an optical device using the optical element(polarization splitting element) according to any one of Embodiments 1to 9. Here, the optical device is a reflection liquid crystal projector.

FIG. 9 is a schematic structural view showing the optical deviceaccording to Embodiment 10 and shows a reflection image modulatingdevice using the polarization splitting element according to any one ofEmbodiments 1 to 9. In FIG. 9, the reflection image modulating deviceincludes a light source 1 composed of a high-pressure mercury lamp orthe like, a reflector 2 for radiating light from the light source 1 in apredetermined direction, and an integrator 3 for forming an illuminationregion having substantially uniform illumination intensity. Theintegrator 3 is composed of fly eye lenses 3 a and 3 b, which can bereplaced with a configuration including a plurality of cylindrical lensarrays. The reflection image modulating device further includes apolarization converting element 4 for adjusting no-polarized light in apredetermined polarization direction, a condenser lens 5 for condensingillumination light, a mirror 6, a field lens 7 for converting theillumination light into telecentric light, and a dichroic mirror 8 fortransmitting light having a wavelength in green wavelength region. Thereflection image modulating device further includes polarizationsplitting elements 9 a 1, 9 b 1, and 9 c 1 according to any one ofEmbodiments 1 to 9, each of which has a characteristic in which theS-polarized light is reflected and the P-polarized light is transmitted,and polarization splitting prisms 9 a, 9 b, and 9 c each having thepolarization splitting elements 9 a 1, 9 b 1, and 9 c 1. The reflectionimage modulating device further includes color selecting phasedifference plates 10 a and 10 b for changing (rotating) polarizationdirections of light beams having predetermined wavelength regions by90°, reflection liquid crystal display elements 11 r, 11 g, and 11 b forreflecting respective incident illumination light beams and modulatingthe light beams based on image signals to produce image light beams, ¼phase difference plates 12 r, 12 g, and 12 b, and a projection lenssystem (projecting optical system) 14 for projecting light emitted from¼ phase difference plates onto a predetermined plane (for examplescreen). When the polarization splitting elements according to any oneof Embodiments 1 to 9 are disposed as described above, an incident anglecharacteristic and a wavelength characteristic are made superior. As aresult, a reflection liquid crystal projector in which contrast obtainedby the entire optical system is very high can be realized.

This application claims priority from Japanese Patent Application No.2004-139054 filed on May 7, 2004 and Japanese Patent Application No.2004-149224 filed on May 19, 2004, which are hereby incorporated byreference herein.

1. An optical element, comprising: a first periodic structure having aperiod shorter than a wavelength of used light; a second periodicstructure that has a period shorter than the wavelength of the usedlight and in which a direction of the period is orthogonal to orsubstantially orthogonal to that of the first periodic structure, thesecond periodic structure being adjacent to the first periodicstructure; and a pair of optical elements disposed so as to sandwich thefirst periodic structure and the second periodic structure, wherein thefirst periodic structure and the second periodic structure transmitlight having first polarization direction and reflect light havingsecond polarization direction orthogonal to the first direction, andwherein the second polarization direction is substantially parallel toone of the periodic direction of the first periodic structure and theperiodic direction of the second periodic structure.
 2. An opticalelement according to claim 1, wherein the used light has a wavelengthbetween 400 nm and 700 nm.
 3. An optical element according to claim 1,wherein the following conditions are satisfied,n1p<n1s,n2p>n2s,|n1s−n2s|>|n1p−n2p|, where n1p and n1s represent effective refractiveindices of the first periodic structure with respect to P-polarizedlight and S-polarized light, respectively, and n2p and n2s representeffective refractive indices of the second periodic structure withrespect to the P-polarized light and the S-polarized light,respectively.
 4. An optical element according to claim 1, wherein thefollowing condition is satisfied,0.95<n1p/n2p<1.2, where n1p and n1s represent effective refractiveindices of the first periodic structure with respect to P-polarizedlight and S-polarized light, respectively.
 5. An optical elementaccording to claim 1, wherein each of the first periodic structure andthe second periodic structure is made of dielectric.
 6. An opticalelement according to claim 5, wherein the dielectric is titanium oxide.7. An optical element according to claim 1, wherein light which is madeincident on the first periodic structure includes a light beam which ismade incident on the first periodic structure at a Brewster's angledetermined based on effective refractive indices of the first periodicstructure and the second periodic structure with respect to P-polarizedlight.
 8. An optical element according to claim 1, wherein light whichis made incident on the first periodic structure includes a light beamwhich is made incident on the first periodic structure at an angle notsmaller than a critical angle determined based on effective refractiveindices of the first periodic structure and the second periodicstructure with respect to S-polarized light.
 9. An optical elementaccording to claim 1, wherein the following condition is satisfied,(n1s·d ₁·con θ)/λs<0.5, where n1s represents the effective refractiveindex of the first periodic structure with respect to the S-polarizedlight, d₁ represents a thickness thereof, λs represents a shortestwavelength of the used light which is made incident on the firstperiodic structure, and θ represents an incident angle thereof.
 10. Anoptical element according to claim 1, wherein the following condition issatisfied,0.2<d ₂ /λs<1.0, where d₂ represents a thickness of the second periodicstructure, λs represents the shortest wavelength of the used light whichis made incident on the first periodic structure, and θ represents theincident angle thereof.
 11. An optical element according to claim 1,wherein each of the first periodic structure and the second periodicstructure is a grating made of dielectric, and the following conditionsare satisfied,0.3<f1<1.0,0.10<f2<0.5, where f1 represents a filling factor which is a ratiobetween the period of the first periodic structure and a width of acorresponding grating and f2 represents a filling factor which is aratio between the period of the second periodic structure and a width ofa corresponding grating.
 12. An optical element according to claim 1,wherein the period of the first periodic structure and the period of thesecond periodic structure are different from each other.
 13. An opticaldevice, comprising: an optical element according to claim 1; modulationmeans for modulating light emitted from the optical element based on animage signal; and a projection optical system for projecting the lightmodulated by the modulation means to a predetermined plane.
 14. Anoptical element, comprising: a first periodic structure having a periodshorter than a wavelength of used light; and a second periodic structurethat has a period shorter than the wavelength of the used light and inwhich a direction of the period is orthogonal to or substantiallyorthogonal to that of the first periodic structure, the second periodicstructure being adjacent to the first periodic structure, wherein theperiod of the first periodic structure and the period of the secondperiodic structure are different from each other.
 15. An optical elementaccording to claim 14, wherein with respect to a first plane including aperiodic direction of the first periodic structure and a normal to aplane of the first periodic structure and a second plane including aperiodic direction of the second periodic structure and a normal to aplane of the second periodic structure, the period of the periodicstructure in one of the first and second planes in which a maximalincident angle of a used light beam is larger than that in the otherplane is smaller than the period of the other periodic structure in theother plane of the first and second planes.
 16. An optical elementaccording to claim 14, wherein with respect to a first plane including aperiodic direction of the first periodic structure and a normal to aplane of the first periodic structure and a second plane including aperiodic direction of the second periodic structure and a normal to aplane of the second periodic structure, the period of the periodicstructure in one of the first and second planes which is closer toparallel to the used light than the other plane is smaller than theperiod of the other periodic structure in the other plane of the firstand second planes.
 17. An optical element according to claim 14, whereinwith defining a representative light beam as a light beam which isemitted from the optical element and passes through an optical axis ofthe optical system, with respect to a first plane including a periodicdirection of the first periodic structure and a normal to a plane of thefirst periodic structure and a second plane including a periodicdirection of the second periodic structure in the optical element and anormal to a plane of the first periodic structure, the period of theperiodic structure in one of the first and second planes which is closerto parallel to the representative light beam than the other plane issmaller than the period of the other periodic structure in the otherplane of the first and second planes.
 18. An optical device, comprising:an optical element according to claim 14; modulation means formodulating light emitted from the optical element based on an imagesignal; and a projection optical system for projecting the lightmodulated by the modulation means to a predetermined plane.